Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ahcm)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.ahcm.01

Input Form

HypergeometricPFQ[{3/2, 6}, {-(7/2), 11/2}, z] == (1/(640 z^4)) (3 (705600 - 348600 z + 124560 z^2 - 35640 z^3 + 8500 z^4 - 1755 z^5 + 340 z^6 - 88 z^7 + 112 z^8 + 16 z^9)) + (1/(1280 z^(9/2))) (3 E^z Sqrt[Pi] (-705600 + 819000 z - 482400 z^2 + 192600 z^3 - 58500 z^4 + 14355 z^5 - 2950 z^6 + 520 z^7 - 80 z^8 + 240 z^9 + 32 z^10) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]